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# chapter13 - Chapter 13 The Accuracy of Averages 13.1...

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Chapter 13 The Accuracy of Averages 13.1 Estimators and estimates As its name suggests, the aim of estimation is to determine the approximate value of the population parameter on the basis of a sample statistic, which is the essence of statistical inference. It is important to differentiate however between an estimator and an estimate . Roughly, an estimator is a rule of finding an estimate of a population parameter. In other words, we find an estimate of a population parameter by employing a certain estimator. In statistics, it is desirable to use a good estimator. Two important criteria for making some judgment of estimators are 1) unbiasedness and 2) efficiency or minimum variance. An estimator is said to be unbiased if the average value of all the es- timates is equal to the population parameter being estimated. For exam- ple, the arithmetic average X = 1 n X i is an unbiased estimator of the population mean, μ . In contrast, the standard deviation calculated by 1 n ( X - X ) 2 is a biased estimator of the population standard deviation.

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